Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}7x-5y &= 3 \\ -9x+3y &= 3\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-9x = -3y+3$ Divide both sides by $-9$ to isolate $x$ $x = {\dfrac{1}{3}y - \dfrac{1}{3}}$ Substitute this expression for $x$ in the first equation. $7({\dfrac{1}{3}y - \dfrac{1}{3}}) - 5y = 3$ $\dfrac{7}{3}y - \dfrac{7}{3} - 5y = 3$ Simplify by combining terms, then solve for $y$ $-\dfrac{8}{3}y - \dfrac{7}{3} = 3$ $-\dfrac{8}{3}y = \dfrac{16}{3}$ $y = -2$ Substitute $-2$ for $y$ in the top equation. $7x-5( -2) = 3$ $7x+10 = 3$ $7x = -7$ $x = -1$ The solution is $\enspace x = -1, \enspace y = -2$.